Octahedral norms and convex combination of slices in Banach spaces

Guerrero, Julio Becerra; López-Pérez, Ginés; Zoca, Abraham Rueda

doi:10.1016/j.jfa.2013.09.004

Cited by 39 publications

(40 citation statements)

References 12 publications

(16 reference statements)

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“…Banach spaces which are 2‐average rough are exactly the octahedral ones (see , , and ). A weaker version of octahedrality was introduced in and it was shown that a Banach space X is weakly octahedral if and only if the diameter of every non‐empty relatively weak* open subset of

B_{X^{*}}

is 2 [, Theorem 2.8].…”

Section: Introductionmentioning

confidence: 99%

Rough norms in spaces of operators

Haller

Langemets

Põldvere

2017

Mathematische Nachrichten

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We investigate sufficient and necessary conditions for the space of bounded linear operators between two Banach spaces to be rough or average rough. Our main result is that L(X,Y) is δ‐average rough whenever X* is δ‐average rough and Y is alternatively octahedral. This allows us to give a unified improvement of two theorems by Becerra Guerrero, López‐Pérez, and Rueda Zoca [J. Math. Anal. Appl. 427 (2015)].

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B_{X^{*}}

is 2 [, Theorem 2.8].…”

Section: Introductionmentioning

confidence: 99%

Rough norms in spaces of operators

Haller

Langemets

Põldvere

2017

Mathematische Nachrichten

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“…In the same paper he asks if the converse is true (Remark (c) on page 119). Since there is no proof included in [5], new proofs appeared, independently, in [6] and [7], in connection with a new study of spaces where all nite convex combination of slices of B X has diameter 2.…”

Section: Introductionmentioning

confidence: 99%

Two properties of Müntz spaces

Abrahamsen

Leraand

Martiny

et al. 2017

Demonstratio Mathematica

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“…Proof. The equivalence between the assertions (i) to (vi), and between (vii) and (viii), were written in [1]. The equivalence between (i) and (viii) is the Theorem 4.2.…”

Section: Resultsmentioning

confidence: 99%

“…A Banach space X has the strong diameter two property if every convex combination of slices in B X , the unit ball of X, has diameter two. It is known that a dual Banach space X * is octahedral if, and only if, X satisfies the strong diameter two property [1], which gives a complete duality relation between these two properties.…”

Section: Introductionmentioning

confidence: 99%

Bidual Octahedral Renormings and Strong Regularity in Banach Spaces

Langemets¹,

López-Pérez²

2019

J. Inst. Math. Jussieu

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We prove that every separable Banach space containing an isomorphic copy of ℓ 1 can be equivalently renormed so that the new bidual norm is octahedral. This answers, in the separable case, a question in Godefroy (1989) [6]. As a direct consequence, we obtain that every dual Banach space, with a separable predual and failing to be strongly regular, can be equivalently renormed with a dual norm to satisfy the strong diameter two property.2010 Mathematics Subject Classification. Primary 46B03, 46B20, 46B22.

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Octahedral norms and convex combination of slices in Banach spaces

Cited by 39 publications

References 12 publications

Rough norms in spaces of operators

Rough norms in spaces of operators

Two properties of Müntz spaces

Bidual Octahedral Renormings and Strong Regularity in Banach Spaces

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